Trigonometry Puzzle: Solving the Challenging Image Puzzle on Etienne.nu

[slipF]

http://www.etienne.nu/imagepuz/4845.htm

How would I go about solving this? I know it involes trigonometry, but I donnot know how to get the proper answer.

 

[hypermorphism]

http://www.etienne.nu/imagepuz/4845.htm

How would I go about solving this? I know it involes trigonometry, but I donnot know how to get the proper answer.

Draw a diagram involving the circle representing the Earth, two conveniently chosen radii, and the chord of interest.

 

[slipF]

sorry, I don't know where to take it from there

 

[hypermorphism]

sorry, I don't know where to take it from there

So you've drawn a diagram ? Which particular radii did you use ? (Look for right-triangles).

 

[slipF]

you would use the radius of the Earth and 35, would you not

 

[hypermorphism]

you would use the radius of the Earth and 35, would you not

Yep. But note that the radius that bisects your 70km chord has two parts, the part above the chord is the length you're looking for. You can find this part by finding the length of the part underneath the chord. My plan would be to draw another radius to connect to one endpoint of the chord. This creates a right triangle created from that radius, the unknown length of the other radius that lies between the chord and the center of the Earth, and half the chord. A diagram is always useful in solving geometry problems.

 

[slipF]

ah, thankyou! pythagorean theorem. Thanks a lot :)